Sacrifices, an obligation to the gods

The
Romans were convinced that, not only you had the obligation to make
sacrifices to the gods, but you could as it were order things
from the gods by offering.

(Human?) sacrifices
These offerings could be very small, but on several occasions a Roman
consul has offered his life, in order to win a
battle. Not just by loosing his life, but dedicating
himself to the death.
He had to fulfill a specific ritual and after that he would seek the
death in the battle. See Livius (8.9)

Human sacrifices
were not very common in Rome, but they did happen.
Even in the above described situation, one can speak of a human
sacrifice, because the augurs had observed bad omens and said that one of the two consuls had to devote himself to the death.

In times of great dangers the Sibylline
books
were consulted. Occasionally was concluded that a human sacrifice was
needed avert the dangers. In the two examples known, the smart Romans
offered a foreign couple. They buried them alive.

Private sacrifices
Much more common were the offerings the father of the family (pater
familias)would bring to the Lares
at the lararium (house altar) in his house. Here he sacrificed food or
drinks mostly wine and would ask to keep his family save or even more
specific personal requests.

Public offerings
were made in the open air, in front of the temple of the god to whom
the sacrifice was made. Here it was extremely important that the
ritual was carried out exactly as prescribed, the prayers were said
exactly correct. If one, even small mistake was made then the whole
ceremony had to be repeated. See for example Livius (2.36-37)

In public sacrifices mostly a domestic animal was killed; or more
animals. At some occasions a hundred or more animals were offered. The
animal had to be free of flaws or defects. The species and color
depended on the god to whom the offering was made. In his book Roman
antiquities 7.72.15 Dionysius of Halicarnassas describes how the
ox, that had to be willing, was led in a procession to the altar.
Here the animal was sprinkled with wine and the mola salsa prepared by
the Priestesses
of Vesta. Then the animal was killed. Not by a priest or magistrate
but by a victimarius, who also butchered the beast. Then the haruspex
inspected the entrails. If the entrails, especially the liver, were
perfect or auspicious, the sacrifice had been accepted by the god and
the offering a success. All this time the priest had to utter the
prescribed prayers and a flute was played, so the priest could not hear
anything wrong. If he did hear anything wrong....
Or if he lost his miter

Was the offering accepted by the god, then the entrails and some other
parts of the beast were burned at the altar. The rest of the meat was
cooked and eaten by the attendant of the offer and the god was content
with the smoke.
If not, it was a bad omen the god was angry and the whole ceremony had
to be repeated the next day or worse.